 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ib/paper-4/17h/c/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

\sum_{i} {Y_{i} - \overset{α}{^}^{'} - \hat{β}^{'} (x_{i} - \overset{x}{ˉ})} = 0.

Because the centered predictors sum to zero,

\overset{α}{^}^{'} = \overset{ˉ}{Y} .

Meanwhile

\overset{α}{^} = \overset{ˉ}{Y} - \hat{β} \overset{x}{ˉ}

, so the two intercept estimates are unequal in general. The parameters themselves satisfy

α^{'} = α + β \overset{x}{ˉ}

 New to topics? Read the docs here!